---
title: "Exploration 3.4"
output: word_document
---
  

```{r setup, include=FALSE}
knitr::opts_knit$set(global.par = TRUE)
knitr::opts_chunk$set(fig.width=4, fig.height=2.67) 
load(url("http://www.isi-stats.com/isi2/ISI.RData"))
```

**Load the hopelessness dataset, e.g.,**
```{r}
hopelessness= read.delim("http://www.isi-stats.com/isi2/data/hopelessness8months_2group.txt", stringsAsFactors=T)
head(hopelessness)
```

**3) Explore the data**
```{r}
with(hopelessness, plot(hopelessness8 ~ Exercise))
```

**3) Is there preliminary evidence of a relationship between Exercise Status and hopelessness level?**


**Statistical model**
```{r}
#effects coding
with(hopelessness, lm(hopelessness8 ~ Exercise, contrasts = list(Exercise="contr.sum")))
```
**4) What are the estimated effects for exercisers and non-exercisers?**


##5) ANOVA table**
```{r}
with(hopelessness, summary(aov(hopelessness8~Exercise)))
```
**How much of the variation in hopelessness scores is explained by whether or not the
individual exercises?**

**6) Explain how baseline hopelessness levels (Not hopeless vs. Moderate to Severe Hopelessness) could act as a confounding variable on the relationship between exercise and eight-month hopelessness.**


**two variable model**
```{r}
model1 = with(hopelessness, lm(hopelessness8~Exercise + BaselineGroup, contrasts = list(Exercise="contr.sum", BaselineGroup="contr.sum")))
summary(model1)
anova(model1)
```
**two variable model with interaction**
```{r}
model2 = with(hopelessness, lm(hopelessness8~Exercise*BaselineGroup, contrasts = list(Exercise="contr.sum", BaselineGroup="contr.sum")))
summary(model2)
anova(model2)
```

**Residuals**
```{r}
hist(model2$residuals)
plot(model2$residuals~model2$fitted.values)
plot(model2)
```